The former Labour politician, premier from 1997 to 2007, allegedly advised taking sleeping pills during an hour-long conversation with Mrs Brooks in July 2011, according to an email she sent her boss James Murdoch, jurors at the Old Bailey, London, heard.
According to Mrs Brooks, Mr Blair advised her not to make "rash short-term solutions as they only give you long-term headaches".
Instead, the former editor of the News Of The World and The Sun told Mr Murdoch that Mr Blair suggested holding an independent inquiry that would report back and clear their names in due course.
Mr Blair also allegedly told Mrs Brooks: "It will pass. Tough up."
Prosecutor Andrew Edis, QC, read to the jury an email Mrs Brooks sent to Mr Murdoch on July 11, 2011, just days before she was arrested by police.
In it, she relayed the telephone conversation she had with Mr Blair.
The court heard Mrs Brooks's notes of the conversation were emailed to Mr Murdoch on July 11. They stated Mr Blair had suggested she form an independent unit with an independent QC, possibly former Director of Public Prosecutions Ken Macdonald, and other legal advisers to investigate and then publish a report like Lord Hutton. The judge had led a controversial inquiry into the death of Government scientist David Kelly.
According to the document, Mr Blair also urged Mrs Brooks to use sleeping pills to keep her head clear.
It said she had counselled the newspaper executive to "tough up" and the scandal would "pass".
In it, Mrs Brooks suggested Mr Blair would act as "unofficial adviser" to James Murdoch and his father Rupert, but added his involvement would need to be "between us".
In the same email chain sent the day after the final edition of the News Of The World was published, Mrs Brooks relayed to Mr Murdoch the news that circulation figures for the Sunday tabloid were still close to four million, saying, "So much for a sales boycott".
James Murdoch, who was chief executive of News International before Mrs Brooks, replied at 3.53pm: "What are you doing on email?"
Earlier, the court heard evidence that Sally Anderson - a friend of former home secretary David Blunkett - admitted giving details of their relationship to newspapers.
The trial had previously heard furious voicemail messages left for Ms Anderson by Mr Blunkett in 2005 - while he was a member of Mr Blair's Government - in which the politician said he hoped whoever leaked information to the media would "rot in hell".
In one message, he said: "Someone very, very close has done a really phenomenal piece of work on destroying both our lives at this moment in time and it's vile."
But prosecutor Mr Edis read a list of agreed facts to the court, in which it was revealed Ms Anderson and/or a friend using her phone contacted the press to tip them off about meetings between the couple - and that they had not been lovers.
Mr Edis said: "(Mr Blunkett's) comments were provoked by publishing an article in the Daily Mail about their close relationship.
"Sally Anderson had actually given information to the Daily Mail.
"A woman calling from Sally Anderson's phone also informed the media about meetings."
He said a woman calling from Ms Anderson's phone later called newsdesks asking for payment for information.
Mr Edis said the Sunday People newspaper ran an article in 2005 about Ms Anderson being pregnant with Mr Blunkett's baby before he "abandoned" her.
The court heard the politician subsequently sued the newspaper and Ms Anderson for libel, resulting in the woman and several media outlets issuing full public apologies, denying she and Mr Blunkett had been lovers.
"David Blunkett was not my lover and could not have made me pregnant," Ms Anderson admitted.
All defendants, including Mrs Brooks, 45, of Churchill, Oxfordshire, deny all charges in the trial.
The trial continues.